WASHINGTON — Within days, the Supreme Court is expected to issue a series of decisions that could transform three fundamental social institutions: marriage, education and voting.

The extraordinary run of blockbuster rulings due in the space of a single week will also reshape the meaning of legal equality and help define for decades to come one of the Constitution’s grandest commands: “the equal protection of the laws.”

If those words require only equal treatment from the government, the rulings are likely to be a mixed bag that will delight and disappoint liberals and conservatives in equal measure. Under that approach, same-sex couples who want to marry would be better off at the end of the term, while blacks and Hispanics could find it harder to get into college and to vote.

But a tension runs through the cases, one based on different conceptions of equality. Some justices are committed to formal equality. Others say the Constitution requires a more dynamic kind of equality, one that takes account of the weight of history and of modern disparities.

The four major cases yet to be decided concern same-sex marriage, affirmative action in higher education and the fate of the Voting Rights Act of 1965, which places special burdens on states with a history of racial discrimination.

Formal equality would require that gay couples be treated just like straight couples when it comes to marriage, white students just like black students when it comes to admissions decisions and Southern states just like Northern ones when it comes to federal oversight of voting. The effect would be to help gay couples, and hurt blacks and Latinos.

But such rulings — “liberal” when it comes to gay rights, “conservative” when it comes to race — are hard to reconcile with the historical meaning of the 14th Amendment’s equal protection clause, adopted in the wake of the Civil War and meant to protect the newly freed black slaves. It would be odd, said David A. Strauss, a law professor at the University of Chicago, for that amendment to help gays but not blacks.

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Abigail Fisher is challenging affirmative action, saying the University of Texas should not classify people on the basis of race.Credit
Luke Sharrett for The New York Times

“What’s weird about it would be the retreat on race, which is the paradigm example of what the 14th Amendment is meant to deal with,” he said, “coupled with fairly aggressive action on sexual orientation.”

But actual as opposed to formal racial equality has fallen out of favor in some circles, Professor Strauss said. “One thing that seems to be going on with these historically excluded groups,” he said, “is that they come to be thought of as just another interest group. Blacks seem to have crossed that line.”

Justice Antonin Scalia appeared to express that view during the argument in February in the voting rights case, Shelby County v. Holder, No. 12-96. “Whenever a society adopts racial entitlements,” he said, “it is very difficult to get out of them through the normal political processes.”

Gay men and lesbians have yet to achieve formal legal equality. They are not protected against job discrimination in much of the nation, may not marry their same-sex partners in most of it and do not have their marriages recognized by the federal government in any of it. The fact that they are asking for equal treatment may help their cause in the cases challenging the federal Defense of Marriage Act, or DOMA, which for purposes of federal benefits defines marriage as the union of a man and a woman, and Proposition 8, the California voter initiative that banned same-sex marriage there.

But Chief Justice John G. Roberts Jr. suggested in March that ordinary politics would sort things out. “As far as I can tell,” he told a lawyer challenging the federal marriage law in United States v. Windsor, No. 12-307, “political figures are falling over themselves to endorse your side of the case.”

In the three months since that argument, threemorestates have adopted same-sex marriage, raising the total to 12, along with the District of Columbia.

Kenji Yoshino, a law professor at New York University, said the two different conceptions of equal protection are animated by different concerns. One is skeptical of government classifications based on race and similar characteristics, whatever their goals. The other tries to make sure that historically disfavored groups are not subordinated.

Defenders of the university’s affirmative action program say the purpose of the classification must figure in the equal protection analysis. “What we’re really trying to do is try to make sure there aren’t castes in our society, and we will try to lift up castes,” Professor Yoshino said.

Whichever side loses a major Supreme Court case is likely to say the decision was an example of judicial activism. That term can be an empty insult, but political scientists try to give it meaning. They say a court is activist when it strikes down a law as unconstitutional. There is a chance the court will be activist in that sense twice this week.

It may strike down central provisions of the federal marriage law and of the Voting Rights Act. Should that happen, said Pamela Harris, an adviser to the Supreme Court Institute at Georgetown’s law school, “the left will be saying out of one side of its mouth, ‘How dare you strike down the considered judgment of Congress in the Voting Rights Act?’ ” In the same breath, she said, liberals will add, “But great job on DOMA.”

There is another possibility: one or more of the cases could fizzle, said Walter E. Dellinger, who served as acting solicitor general in the Clinton administration and filed an influential brief in the Proposition 8 case, Hollingsworth v. Perry, No. 12-144. It argued that the failure of officials in California to appeal the judgment against them deprived the Supreme Court of jurisdiction to decide the case, and it was discussed at the argument in March.

Mr. Dellinger said all four remaining blockbuster cases suffer from plausible procedural flaws that could lead to their dismissal. “I’ve never heard of this before,” he said of such an end-of-term possibility.

An effort to harmonize all of the court’s big decisions may in the end prove impossible. “It’s hard to imagine somebody happy with everything they do, except Justice Kennedy,” Professor Strauss said, referring to the member of the court at its ideological center, Justice Anthony M. Kennedy.

That may be just as well for the court’s reputation. In giving something to liberals and something to conservatives, as it often does, Professor Strauss said, “the court has avoided putting itself in a position where either side wants to declare war on them.”

A version of this article appears in print on June 23, 2013, on Page A1 of the New York edition with the headline: Justices Weigh Cases Redefining Legal Equality. Order Reprints|Today's Paper|Subscribe